Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/2888
Título: | Generalized invertibility in two semigroups of a ring |
Autor(es): | Patrício, Pedro Puystjens, Roland |
Palavras-chave: | Generalized invertibility Corner rings Matrices over rings Semigroups |
Data: | 15-Jan-2004 |
Editora: | Elsevier 1 |
Revista: | Linear Algebra and its Applications |
Citação: | "Linear Algebra and its Applications". ISSN 0024-3795. 377 (2004) 125-139. |
Resumo(s): | In {\em Linear and Multilinear Algebra}, 1997, Vol.43, pp.137-150, R. Puystjens and R. E. Hartwig proved that given a regular element $t$ of a ring $R$ with unity $1$, then $t$ has a group inverse if and only if $u=t^{2}t^{-}+1-tt^{-}$ is invertible in $R$ if and only if $v=t^{-}t^{2}+1-t^{-}t$ is invertible in $R$. There, R. E. Hartwig posed the pertinent question whether the inverse of $u$ and $v$ could be directly related. Similar equivalences appear in the characterization of Moore-Penrose and Drazin invertibility, and therefore analogous questions arise. We present a unifying result to answer these questions not only involving classical invertibility, but also some generalized inverses as well. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/2888 |
DOI: | 10.1016/j.laa.2003.08.004 |
ISSN: | 0024-3795 |
Versão da editora: | http://www.elsevier.com/wps/find/journaldescription.cws_home/522483/description#description |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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gismgrp.pdf | 172,29 kB | Adobe PDF | Ver/Abrir |